A hexagonal network structure (honeycomb structure) composed of six-membered rings of carbon atoms, namely benzene rings, combined in a plane is called a graphene sheet. A large number of graphene sheets are stacked to form a graphite crystal. Graphite has high electrical conductivity equivalent to metal because delocalized π electrons can move in graphite via a conjugated system formed along the carbon chains of the hexagonal network structure (if a non-metal material exhibits high electrical conductivity equivalent to metal by, for example, the movement of delocalized π electrons, the material is assumed to be “metallic” in the description below).
On the other hand, a single-walled carbon nanotube is formed by rolling a rectangular graphene sheet into a cylinder and seamlessly combining its sides. The molecular structure of the carbon nanotube varies slightly depending on how the sheet is rolled, and its electrical properties change from semiconductive to metallic accordingly. This point is described below.
FIG. 8 is a developed view (part of a graphene sheet) for defining the molecular structure of a carbon nanotube. This sheet is rolled so that a six-membered ring 51 overlaps with another six-membered ring 52, thereby forming a single-walled carbon nanotube. Specifically, the graphene sheet is rolled so that a line segment A-A′ drawn from a point A on the six-membered ring 51 to a point A′ corresponding to the point A on the six-membered ring 52 becomes the circumference of the resultant cylinder.
The molecular structure of the carbon nanotube depends on the number and orientation of six-membered rings arrayed in the circumferential direction of the cylinder. This is specifically indicated by a pair of integers (n,m) in the following formula:{right arrow over (c)}=n{right arrow over (a)}+m {right arrow over (b)}wherein {right arrow over (c)} is a position vector from the point A to the point A′, and {right arrow over (a)} and {right arrow over (b)} are unit vectors shown in the lower right of FIG. 8.
In FIG. 8, for example,{right arrow over (c)}=8{right arrow over (a)}+2{right arrow over (b)}Thus the structure of the carbon nanotube is identified by the pair of integers (8,2).
Electrons have the properties as waves. Electron waves in molecules may strengthen or weaken each other in relation to their phases. What types of electron waves strengthen or weaken each other depends on the structure of molecules. Accordingly, carbon nanotubes having different structures have different electron states permitted and therefore have different electrical properties.
Quantum mechanical calculations indicate that the electrical properties of carbon nanotubes depend largely on the above pair of integers (n,m). This has also been confirmed by experiment (“Carbon Nanotube” edited by Kazuyoshi Tanaka, Kagaku-Dojin Publishing Company, Inc., 2001, pp. 19-46).
A band gap is the energy difference between the highest occupied molecular orbit (HOMO) and lowest unoccupied molecular orbit (LUMO) of electrons. As n increases, the band gap of carbon nanotubes decreases gradually and approaches that of graphite. As a special case, if (2n+m) is a multiple of 3, the highest occupied molecular orbit (HOMO) and the lowest unoccupied molecular orbit (LUMO) become degenerate, resulting in a band gap of 0. Such a carbon nanotube is metallic.
In summary,
if 2n+m=3×i, the carbon nanotube is metallic if 2n+m≠3×i, the carbon nanotube is semiconductive where i is an integer. The band gap of a semiconductive carbon nanotube decreases as n increases.
Thus carbon nanotubes are an extremely attractive electronic material. They change their electronic properties from semiconductive to metallic according to the size of sheets and how the sheets are rolled, and have the possibility for controlling the band gap, which determines the performance of semiconductor devices.
If the electrical properties of carbon nanotubes become freely adjustable by controlling their structures, carbon nanotubes may replace semiconductors and metals used for many electronic components.
In addition to the above distinct electronic properties, carbon nanotubes have many excellent properties. For example, in an ultrafine linear structure like a carbon nanotube, a phenomenon called ballistic transport occurs in which electrons or holes can move at high speed without being scattered. This phenomenon can dramatically increase the operational speed of electronic components.
In addition, carbon nanotubes have the highest thermal conductivity among all substances. Carbon nanotubes may therefore solve the problem that large-scale integrated circuits (LSIs) that have a higher packing density or operate at a higher speed generate a larger amount of heat which causes malfunctions more readily.
Furthermore, carbon nanotubes have extraordinarily higher tensile and flexural strength than the existing materials. This feature is advantageous in bottom-up microfabrication.
As described above, carbon nanotubes are expected as a material with the potential for breaking through a barrier to achieving higher-speed, finer LSIs in place of conventional semiconductor technology, which is centered on inorganic materials such as silicon, but is approaching its limit.
Studies have already been started to produce electronic devices such as transistors using carbon nanotubes. Among such studies, a field-effect transistor featuring a multi-walled carbon nanotube has recently been proposed in Document 1 (The Chemical Daily, The Chemical Daily Co., Ltd., Feb. 28, 2002, p. 1).
Carbon nanotubes are classified into a single-walled carbon nanotube, which is a rolled graphene sheet, and a multi-walled carbon nanotube, which includes nested cylindrical carbon nanotubes with different diameters.
In a multi-walled carbon nanotube, inner and outer adjacent layers are separated by a distance of 0.3 to 0.4 nm. The space between the two layers is filled with π electron clouds of carbon atoms constituting six-membered rings of the individual layers. The inner and outer layers are concentrically arranged at a constant distance.
The resistance between the two layers is 100 to 10,000 times the resistance of each layer of graphene sheet in a plane. The space between the two layers, or more layers, may be used as a gate insulating layer to produce an insulated-gate field-effect transistor.
FIG. 9 is a schematic diagram showing the structure of a field-effect transistor produced using a double-walled carbon nanotube according to Document 1 above (hereinafter referred to as a comparative example).
This field-effect transistor is composed of a double-walled carbon nanotube 61 having an inner semiconductive carbon nanotube layer 1 and an outer metallic carbon nanotube layer 2 partially covering the inner semiconductive carbon nanotube layer 1. A metal source electrode 3 and a metal drain electrode 5 are brought into contact with the semiconductive carbon nanotube layer 1 while a metal gate electrode 4 is brought into contact with the metallic carbon nanotube layer 2.
To implement transistor operation, a control gate voltage VG is applied to the metallic carbon nanotube layer 2 via the gate electrode 4 while a drain-source voltage VDS is applied to the semiconductive carbon nanotube layer 1 between the source electrode 3 and the drain electrode 5.
The application of gate voltage causes the injection of induced charges into the semiconductive carbon nanotube layer 1 to control the conductivity of the semiconductive carbon nanotube layer 1 between the source electrode 3 and the drain electrode 5, thereby implementing transistor operation. The space between the semiconductive carbon nanotube layer 1 and the metallic carbon nanotube layer 2 functions as an insulating layer included in a general insulated-gate field-effect transistor.
FIG. 2 shows the current-voltage (drain current ID to drain-source voltage VDS) characteristics of the field-effect transistor according to the comparative example. The drain current ID increases as the drain-source voltage VDS is increased in a low region with the gate voltage VG kept constant. The drain current ID then approaches saturation, and essentially becomes constant irrespective of the voltage VDS after the voltage VDS exceeds a certain level.
In the saturation region, the drain current ID increases with increasing gate voltage VG. The transistor operation can therefore be implemented by modulating the drain current ID with the gate voltage VG (the control voltage applied to the gate electrode 4).
The field-effect transistor according to the comparative example, however, provides low saturated drain current ID, and therefore exhibits a low rate of increase to changes in the gate voltage VG. The application of gate voltage therefore has a small effect of amplifying the drain current ID. This leads to high power consumption.
This is probably because the semiconductive carbon nanotube layer 1 of the transistor according to the comparative example, as shown in FIG. 9, has regions 62 that are not included in the metallic carbon nanotube layer 2 between the source electrode 3 and the drain electrode 5. These regions 62 make it difficult to form a uniformly continuous channel between the source electrode 3 and the drain electrode 5 because the regions 62 are beyond the action of the gate voltage VG.
Next, a study is made on the possibility for achieving the transistor operation of the transistor according to the comparative example by supplying current through the regions 62 beyond the action of the gate voltage VG using a tunneling effect. Specifically, the probability that the tunneling effect allows electrons to pass through the regions 62 beyond the action of the gate voltage VG is calculated with varying bias voltage E, where the regions 62 have a length of L m (the distance between the source electrode 3 or drain electrode 5 and the metallic carbon nanotube layer 2).
Single-walled carbon nanotubes have a work function of 5.15 eV (M. Shiraishi and M. Ata, Carbon, 39, 1913-1917 (2001)) and a band gap of 0.1 to 1.4 eV (C. H. Olk and J. P. Heremans, J. Material Res., 9, 259 (1994); C. T. White, D. H. Roberston, and J. W. Mintmire, Phys. Rev. B, 47, 5485 (1993)). In this calculation, the semiconductive carbon nanotube layer 1 is assumed to have a band gap of 0.4 eV.
The electrode material used is gold, which has a work function of 5.05 eV. Accordingly, an energy barrier V0 of 0.1 eV occurs between the gold electrodes and the semiconductive carbon nanotube layer 1 on the assumption that the semiconductive carbon nanotube layer 1 is an intrinsic semiconductor.
Referring to FIG. 10A, when electrons pass through an energy barrier having a height of V0 eV and a thickness of L m by the tunneling effect with a constant bias voltage E applied to the gold electrodes, a transmission probability T is given by the following formula (1):
                              T          =                                                    4                ⁢                                                      k                    2                                    /                                      κ                    2                                                                                                                    (                                          1                      -                                                                        k                          2                                                /                                                  κ                          2                                                                                      )                                    ⁢                                      sinh                    2                                    ⁢                  κ                  ⁢                                                                          ⁢                  L                                +                                  4                  ⁢                                                            (                                              k                        /                        κ                                            )                                        2                                    ⁢                                      cosh                    2                                    ⁢                  κ                  ⁢                                                                          ⁢                  L                                                                    ⁢                                  ⁢        wherein        ⁢                                  ⁢                  k          =                                                    2                ⁢                m                ⁢                                                                  ⁢                E                                            ℏ                2                                                    ⁢                                  ⁢                              κ            ⁢                                                  ⁢            i                    =                                                    2                ⁢                                  m                  ⁡                                      (                                          E                      -                                              V                        0                                                              )                                                                              ℏ                2                                                                        (        1        )            and m is the electron mass, namely 9.1×10−31 kg.
If E<V0, κi is an imaginary number, and T in the formula (1) decreases exponentially with increasing L. In other words, if the distance L is large, few electrons can enter the region of the semiconductive carbon nanotube layer 1, and eventually the electrons are totally reflected. The thickness (coherence length) for allowing electrons to pass through an energy barrier of 0.01 eV by the tunneling effect, that is, for allowing the formula (1) to converge, is about 2 nm according to the calculation.
Next, changes in the transmission probability T in response to changes in the height (V0−E) of the barrier for electrons when L is 1.5 nm, 1 nm, and 0.5 nm were calculated, and the results are shown in FIG. 10B and Table 1. FIG. 10B and Table 1 indicate that the probability T of the transmission by the tunneling effect decreases with increasing height (V0−E) and length L of the energy barrier. According to FIG. 10B and Table 1, additionally, L must be limited to about 1 nm to achieve a transmission probability T of about 50%.
TABLE 1V0-ETransmission probability (%)(eV)L = 0.5 nmL = 1.0 nmL = 1.5 nm0.0190.563.134.60.0289.560.932.80.0388.358.330.90.0486.755.328.80.0584.651.826.50.0681.747.723.90.0777.642.520.80.0870.835.817.10.0957.926.212.2
As described above, the length L of the regions 62 must at least be limited to about 2 nm or less, preferably about 1 nm or less, to relieve the problem of the regions 62 beyond the action of the gate voltage VG with the aid of the tunneling effect. Such a length seems unattainable in view of processing accuracy.
According to the article of Document 1 above, a semiconductive carbon nanotube including fullerene containing metal atoms is used as the semiconductive carbon nanotube layer 1 to improve conductivity. The effect of improvement by the included fullerene, however, seems small in consideration that the effect by applying gate voltage acts only on an extremely thin layer near the surface of the semiconductive carbon nanotube layer 1.
In light of the above circumstances, an object of the present invention is to provide a microelectronic device that overcomes the disadvantages of known electronic devices composed of carbon molecules and that delivers performance superior to the devices, and also to provide a method for producing the device.